How to prevent model from changing locations when going into dynamic topology mode?
When I load the .blend file, everything in the scene is selected.  

Click on the model name 'Game_engine' in the outliner,
so it selects all the pieces of the model, and it's pose.  

Click the skeleton icon in properties  

click Rest Position  

Alt-R to reset rotation.  

Hope that helps, if not, you might try Autodesk's tool
to convert it to a more recent .fbx file.
http://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&amp;id=22694909  

As a side-note:
The scene seems to have 2 lamps and 2 cameras with the exact same position.
You might delete the extra .001 for each of those, if they aren't needed.